Generated by Cython 0.14.1 on Sat Sep 24 08:10:08 2011
Raw output: _sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.c
1:
2: include "interrupt.pxi" # ctrl-c interrupt block support
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":2 * * include "interrupt.pxi" # ctrl-c interrupt block support #<<<<<<<<<<<<<<* include "stdsage.pxi" # ctrl-c interrupt block support * */ __pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(((PyObject *)__pyx_t_1)); if (PyObject_SetAttr(__pyx_m, __pyx_n_s____test__, ((PyObject *)__pyx_t_1))<0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(((PyObject *)__pyx_t_1)); __pyx_t_1 = 0;
3: include "stdsage.pxi" # ctrl-c interrupt block support
4:
5: include "cdefs.pxi"
6: #auto
7: #from math import exp
8:
9: cdef extern from "math.h":
10: double exp(double x)
11: double cos(double x)
12: double sin(double x)
13: double atan2(double y, double x)
14:
15: cpdef list solve_diffeq(double a, double b, double c, double t0, double y0, double y0p):
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":15 * double atan2(double y, double x) * * cpdef list solve_diffeq(double a, double b, double c, double t0, double y0, double y0p): #<<<<<<<<<<<<<<* """ * Returns a list starting with discriminant */ static PyObject *__pyx_pf_75_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0_solve_diffeq(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/ static PyObject *__pyx_f_75_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0_solve_diffeq(double __pyx_v_a, double __pyx_v_b, double __pyx_v_c, double __pyx_v_t0, double __pyx_v_y0, double __pyx_v_y0p, int __pyx_skip_dispatch) { PyObject *__pyx_v_result = 0; double __pyx_v_discriminant; double __pyx_v_r1; double __pyx_v_r2; double __pyx_v_pos_disc_root; double __pyx_v_y1t0; double __pyx_v_y1difft0; double __pyx_v_y2t0; double __pyx_v_y2difft0; double __pyx_v_denominator; double __pyx_v_c1; double __pyx_v_c2; double __pyx_v_lam; double __pyx_v_mu; double __pyx_v_elam; double __pyx_v_sinmu; double __pyx_v_cosmu; double __pyx_v_r; double __pyx_v_delta; PyObject *__pyx_r = NULL; __Pyx_RefNannySetupContext("solve_diffeq"); /* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":15 * double atan2(double y, double x) * * cpdef list solve_diffeq(double a, double b, double c, double t0, double y0, double y0p): #<<<<<<<<<<<<<<* """ * Returns a list starting with discriminant */ static PyObject *__pyx_pf_75_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0_solve_diffeq(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/ static char __pyx_doc_75_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0_solve_diffeq[] = "File: _sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx (starting at line 15)\n\n Returns a list starting with discriminant\n if discriminant > 0, then the list is [disc, r1, r2, c1, c2]\n if discriminant == 0, then the list is [disc,r1,c1,c2]\n if discriminant<0, then the list is [disc, lambda, mu, c1, c2,r,delta]\n "; 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default: goto __pyx_L5_argtuple_error; } switch (PyTuple_GET_SIZE(__pyx_args)) { case 0: values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__a); if (likely(values[0])) kw_args--; else goto __pyx_L5_argtuple_error; case 1: values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__b); if (likely(values[1])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("solve_diffeq", 1, 6, 6, 1); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } case 2: values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__c); if (likely(values[2])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("solve_diffeq", 1, 6, 6, 2); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } case 3: values[3] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__t0); if (likely(values[3])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("solve_diffeq", 1, 6, 6, 3); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } case 4: values[4] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__y0); if (likely(values[4])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("solve_diffeq", 1, 6, 6, 4); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } case 5: values[5] = PyDict_GetItem(__pyx_kwds, __pyx_n_s__y0p); if (likely(values[5])) kw_args--; else { __Pyx_RaiseArgtupleInvalid("solve_diffeq", 1, 6, 6, 5); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } } if (unlikely(kw_args > 0)) { if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, PyTuple_GET_SIZE(__pyx_args), "solve_diffeq")<0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } __pyx_v_a = __pyx_PyFloat_AsDouble(values[0]); if (unlikely((__pyx_v_a == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_b = __pyx_PyFloat_AsDouble(values[1]); if (unlikely((__pyx_v_b == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_c = __pyx_PyFloat_AsDouble(values[2]); if (unlikely((__pyx_v_c == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_t0 = __pyx_PyFloat_AsDouble(values[3]); if (unlikely((__pyx_v_t0 == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_y0 = __pyx_PyFloat_AsDouble(values[4]); if (unlikely((__pyx_v_y0 == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_y0p = __pyx_PyFloat_AsDouble(values[5]); if (unlikely((__pyx_v_y0p == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} } else if (PyTuple_GET_SIZE(__pyx_args) != 6) { goto __pyx_L5_argtuple_error; } else { __pyx_v_a = __pyx_PyFloat_AsDouble(PyTuple_GET_ITEM(__pyx_args, 0)); if (unlikely((__pyx_v_a == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_b = __pyx_PyFloat_AsDouble(PyTuple_GET_ITEM(__pyx_args, 1)); if (unlikely((__pyx_v_b == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_c = __pyx_PyFloat_AsDouble(PyTuple_GET_ITEM(__pyx_args, 2)); if (unlikely((__pyx_v_c == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_t0 = __pyx_PyFloat_AsDouble(PyTuple_GET_ITEM(__pyx_args, 3)); if (unlikely((__pyx_v_t0 == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L3_error;} __pyx_v_y0 = __pyx_PyFloat_AsDouble(PyTuple_GET_ITEM(__pyx_args, 4)); if (unlikely((__pyx_v_y0 == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; 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__pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_r = __pyx_t_1; __pyx_t_1 = 0; goto __pyx_L0; __pyx_r = Py_None; __Pyx_INCREF(Py_None); goto __pyx_L0; __pyx_L1_error:; __Pyx_XDECREF(__pyx_t_1); __Pyx_AddTraceback("_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.solve_diffeq"); __pyx_r = NULL; __pyx_L0:; __Pyx_XGIVEREF(__pyx_r); __Pyx_RefNannyFinishContext(); return __pyx_r; }
16: """
17: Returns a list starting with discriminant
18: if discriminant > 0, then the list is [disc, r1, r2, c1, c2]
19: if discriminant == 0, then the list is [disc,r1,c1,c2]
20: if discriminant < 0, then the list is [disc, lambda, mu, c1, c2,r,delta]
21: """
22: cdef list result = []
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":22 * if discriminant<0, then the list is [disc, lambda, mu, c1, c2,r,delta] * """ * cdef list result = [] #<<<<<<<<<<<<<<* cdef double discriminant = b*b-4*a*c * cdef double const[2] */ __pyx_t_1 = PyList_New(0); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 22; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(((PyObject *)__pyx_t_1)); __pyx_v_result = __pyx_t_1; __pyx_t_1 = 0;
23: cdef double discriminant = b*b-4*a*c
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":23 * """ * cdef list result = [] * cdef double discriminant = b*b-4*a*c #<<<<<<<<<<<<<<* cdef double const[2] * result.append(discriminant) */ __pyx_v_discriminant = ((__pyx_v_b * __pyx_v_b) - ((4.0 * __pyx_v_a) * __pyx_v_c));
24: cdef double const[2]
25: result.append(discriminant)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":25 * cdef double discriminant = b*b-4*a*c * cdef double const[2] * result.append(discriminant) #<<<<<<<<<<<<<<* cdef double r1, r2, pos_disc_root, y1t0, y1difft0, y2t0, y2difft0, denominator, c1, c2 * cdef double lam, mu, elam, sinmu, cosmu, r, delta */ if (unlikely(__pyx_v_result == Py_None)) { PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 25; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __pyx_t_1 = PyFloat_FromDouble(__pyx_v_discriminant); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 25; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 25; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
26: cdef double r1, r2, pos_disc_root, y1t0, y1difft0, y2t0, y2difft0, denominator, c1, c2
27: cdef double lam, mu, elam, sinmu, cosmu, r, delta
28: if discriminant > 0:
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":28 * cdef double r1, r2, pos_disc_root, y1t0, y1difft0, y2t0, y2difft0, denominator, c1, c2 * cdef double lam, mu, elam, sinmu, cosmu, r, delta * if discriminant > 0: #<<<<<<<<<<<<<<* pos_disc_root = sqrt(discriminant) * r1 = (-b + pos_disc_root)/(2*a) */ __pyx_t_3 = (__pyx_v_discriminant > 0.0); if (__pyx_t_3) {
29: pos_disc_root = sqrt(discriminant)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":29
* cdef double lam, mu, elam, sinmu, cosmu, r, delta
* if discriminant > 0:
* pos_disc_root = sqrt(discriminant) # <<<<<<<<<<<<<<
* r1 = (-b + pos_disc_root)/(2*a)
* r2 = (-b - pos_disc_root)/(2*a)
*/
__pyx_v_pos_disc_root = sqrt(__pyx_v_discriminant);
30: r1 = (-b + pos_disc_root)/(2*a)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":30
* if discriminant > 0:
* pos_disc_root = sqrt(discriminant)
* r1 = (-b + pos_disc_root)/(2*a) # <<<<<<<<<<<<<<
* r2 = (-b - pos_disc_root)/(2*a)
* result.append(r1)
*/
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if (unlikely(__pyx_t_5 == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 30; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_r1 = (__pyx_t_4 / __pyx_t_5);
31: r2 = (-b - pos_disc_root)/(2*a)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":31
* pos_disc_root = sqrt(discriminant)
* r1 = (-b + pos_disc_root)/(2*a)
* r2 = (-b - pos_disc_root)/(2*a) # <<<<<<<<<<<<<<
* result.append(r1)
* result.append(r2)
*/
__pyx_t_5 = ((-__pyx_v_b) - __pyx_v_pos_disc_root);
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PyErr_Format(PyExc_ZeroDivisionError, "float division");
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__pyx_v_r2 = (__pyx_t_5 / __pyx_t_4);
32: result.append(r1)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":32
* r1 = (-b + pos_disc_root)/(2*a)
* r2 = (-b - pos_disc_root)/(2*a)
* result.append(r1) # <<<<<<<<<<<<<<
* result.append(r2)
* y1t0 = exp(r1*t0)
*/
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33: result.append(r2)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":33
* r2 = (-b - pos_disc_root)/(2*a)
* result.append(r1)
* result.append(r2) # <<<<<<<<<<<<<<
* y1t0 = exp(r1*t0)
* y1difft0 = r1*y1t0
*/
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34: y1t0 = exp(r1*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":34
* result.append(r1)
* result.append(r2)
* y1t0 = exp(r1*t0) # <<<<<<<<<<<<<<
* y1difft0 = r1*y1t0
* y2t0 = exp(r2*t0)
*/
__pyx_v_y1t0 = exp((__pyx_v_r1 * __pyx_v_t0));
35: y1difft0 = r1*y1t0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":35
* result.append(r2)
* y1t0 = exp(r1*t0)
* y1difft0 = r1*y1t0 # <<<<<<<<<<<<<<
* y2t0 = exp(r2*t0)
* y2difft0 = r2*y2t0
*/
__pyx_v_y1difft0 = (__pyx_v_r1 * __pyx_v_y1t0);
36: y2t0 = exp(r2*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":36
* y1t0 = exp(r1*t0)
* y1difft0 = r1*y1t0
* y2t0 = exp(r2*t0) # <<<<<<<<<<<<<<
* y2difft0 = r2*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0
*/
__pyx_v_y2t0 = exp((__pyx_v_r2 * __pyx_v_t0));
37: y2difft0 = r2*y2t0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":37
* y1difft0 = r1*y1t0
* y2t0 = exp(r2*t0)
* y2difft0 = r2*y2t0 # <<<<<<<<<<<<<<
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
*/
__pyx_v_y2difft0 = (__pyx_v_r2 * __pyx_v_y2t0);
38: denominator = y1t0*y2difft0 - y2t0*y1difft0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":38
* y2t0 = exp(r2*t0)
* y2difft0 = r2*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0 # <<<<<<<<<<<<<<
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
*/
__pyx_v_denominator = ((__pyx_v_y1t0 * __pyx_v_y2difft0) - (__pyx_v_y2t0 * __pyx_v_y1difft0));
39: c1 = (y0*y2difft0 - y0p*y2t0)/denominator
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":39
* y2difft0 = r2*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator # <<<<<<<<<<<<<<
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1)
*/
__pyx_t_4 = ((__pyx_v_y0 * __pyx_v_y2difft0) - (__pyx_v_y0p * __pyx_v_y2t0));
if (unlikely(__pyx_v_denominator == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 39; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_c1 = (__pyx_t_4 / __pyx_v_denominator);
40: c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":40
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator # <<<<<<<<<<<<<<
* result.append(c1)
* result.append(c2)
*/
__pyx_t_4 = (((-__pyx_v_y0) * __pyx_v_y1difft0) + (__pyx_v_y0p * __pyx_v_y1t0));
if (unlikely(__pyx_v_denominator == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 40; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_c2 = (__pyx_t_4 / __pyx_v_denominator);
41: result.append(c1)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":41
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1) # <<<<<<<<<<<<<<
* result.append(c2)
* elif discriminant == 0:
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 41; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_c1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 41; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 41; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
42: result.append(c2)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":42
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1)
* result.append(c2) # <<<<<<<<<<<<<<
* elif discriminant == 0:
* r1 = -b/(2*a)
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 42; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_c2); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 42; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 42; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
goto __pyx_L3;
}
43: elif discriminant == 0:
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":43 * result.append(c1) * result.append(c2) * elif discriminant == 0: #<<<<<<<<<<<<<<* r1 = -b/(2*a) * result.append(r1) */ __pyx_t_3 = (__pyx_v_discriminant == 0.0); if (__pyx_t_3) {
44: r1 = -b/(2*a)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":44
* result.append(c2)
* elif discriminant == 0:
* r1 = -b/(2*a) # <<<<<<<<<<<<<<
* result.append(r1)
*
*/
__pyx_t_4 = (-__pyx_v_b);
__pyx_t_5 = (2.0 * __pyx_v_a);
if (unlikely(__pyx_t_5 == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 44; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_r1 = (__pyx_t_4 / __pyx_t_5);
45: result.append(r1)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":45
* elif discriminant == 0:
* r1 = -b/(2*a)
* result.append(r1) # <<<<<<<<<<<<<<
*
* y1t0 = exp(r1*t0)
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_r1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 45; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
46:
47: y1t0 = exp(r1*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":47
* result.append(r1)
*
* y1t0 = exp(r1*t0) # <<<<<<<<<<<<<<
* y1difft0 = r1*exp(r1*t0)
* y2t0 = t0*y1t0
*/
__pyx_v_y1t0 = exp((__pyx_v_r1 * __pyx_v_t0));
48: y1difft0 = r1*exp(r1*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":48
*
* y1t0 = exp(r1*t0)
* y1difft0 = r1*exp(r1*t0) # <<<<<<<<<<<<<<
* y2t0 = t0*y1t0
* y2difft0 = y1t0 + r1*y2t0
*/
__pyx_v_y1difft0 = (__pyx_v_r1 * exp((__pyx_v_r1 * __pyx_v_t0)));
49: y2t0 = t0*y1t0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":49
* y1t0 = exp(r1*t0)
* y1difft0 = r1*exp(r1*t0)
* y2t0 = t0*y1t0 # <<<<<<<<<<<<<<
* y2difft0 = y1t0 + r1*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0
*/
__pyx_v_y2t0 = (__pyx_v_t0 * __pyx_v_y1t0);
50: y2difft0 = y1t0 + r1*y2t0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":50
* y1difft0 = r1*exp(r1*t0)
* y2t0 = t0*y1t0
* y2difft0 = y1t0 + r1*y2t0 # <<<<<<<<<<<<<<
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
*/
__pyx_v_y2difft0 = (__pyx_v_y1t0 + (__pyx_v_r1 * __pyx_v_y2t0));
51: denominator = y1t0*y2difft0 - y2t0*y1difft0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":51
* y2t0 = t0*y1t0
* y2difft0 = y1t0 + r1*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0 # <<<<<<<<<<<<<<
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
*/
__pyx_v_denominator = ((__pyx_v_y1t0 * __pyx_v_y2difft0) - (__pyx_v_y2t0 * __pyx_v_y1difft0));
52: c1 = (y0*y2difft0 - y0p*y2t0)/denominator
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":52
* y2difft0 = y1t0 + r1*y2t0
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator # <<<<<<<<<<<<<<
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1)
*/
__pyx_t_5 = ((__pyx_v_y0 * __pyx_v_y2difft0) - (__pyx_v_y0p * __pyx_v_y2t0));
if (unlikely(__pyx_v_denominator == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 52; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_c1 = (__pyx_t_5 / __pyx_v_denominator);
53: c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":53
* denominator = y1t0*y2difft0 - y2t0*y1difft0
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator # <<<<<<<<<<<<<<
* result.append(c1)
* result.append(c2)
*/
__pyx_t_5 = (((-__pyx_v_y0) * __pyx_v_y1difft0) + (__pyx_v_y0p * __pyx_v_y1t0));
if (unlikely(__pyx_v_denominator == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 53; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_c2 = (__pyx_t_5 / __pyx_v_denominator);
54: result.append(c1)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":54
* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1) # <<<<<<<<<<<<<<
* result.append(c2)
* else:
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 54; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_c1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 54; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 54; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
55: result.append(c2)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":55
* c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
* result.append(c1)
* result.append(c2) # <<<<<<<<<<<<<<
* else:
* lam = -b/(2*a)
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 55; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_c2); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 55; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 55; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
goto __pyx_L3;
}
/*else*/ {
56: else:
57: lam = -b/(2*a)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":57
* result.append(c2)
* else:
* lam = -b/(2*a) # <<<<<<<<<<<<<<
* mu = sqrt(-discriminant)/(2*a)
* result.append(lam)
*/
__pyx_t_5 = (-__pyx_v_b);
__pyx_t_4 = (2.0 * __pyx_v_a);
if (unlikely(__pyx_t_4 == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 57; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_lam = (__pyx_t_5 / __pyx_t_4);
58: mu = sqrt(-discriminant)/(2*a)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":58
* else:
* lam = -b/(2*a)
* mu = sqrt(-discriminant)/(2*a) # <<<<<<<<<<<<<<
* result.append(lam)
* result.append(mu)
*/
__pyx_t_4 = sqrt((-__pyx_v_discriminant));
__pyx_t_5 = (2.0 * __pyx_v_a);
if (unlikely(__pyx_t_5 == 0)) {
PyErr_Format(PyExc_ZeroDivisionError, "float division");
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 58; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_v_mu = (__pyx_t_4 / __pyx_t_5);
59: result.append(lam)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":59
* lam = -b/(2*a)
* mu = sqrt(-discriminant)/(2*a)
* result.append(lam) # <<<<<<<<<<<<<<
* result.append(mu)
* elam = exp(lam*t0)
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 59; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_lam); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 59; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 59; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
60: result.append(mu)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":60
* mu = sqrt(-discriminant)/(2*a)
* result.append(lam)
* result.append(mu) # <<<<<<<<<<<<<<
* elam = exp(lam*t0)
* cosmu = cos(mu*t0)
*/
if (unlikely(__pyx_v_result == Py_None)) {
PyErr_SetString(PyExc_AttributeError, "'NoneType' object has no attribute 'append'"); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 60; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_t_1 = PyFloat_FromDouble(__pyx_v_mu); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 60; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
__pyx_t_2 = PyList_Append(__pyx_v_result, __pyx_t_1); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 60; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
61: elam = exp(lam*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":61
* result.append(lam)
* result.append(mu)
* elam = exp(lam*t0) # <<<<<<<<<<<<<<
* cosmu = cos(mu*t0)
* sinmu = sin(mu*t0)
*/
__pyx_v_elam = exp((__pyx_v_lam * __pyx_v_t0));
62: cosmu = cos(mu*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":62
* result.append(mu)
* elam = exp(lam*t0)
* cosmu = cos(mu*t0) # <<<<<<<<<<<<<<
* sinmu = sin(mu*t0)
* y1t0 = elam*cosmu
*/
__pyx_v_cosmu = cos((__pyx_v_mu * __pyx_v_t0));
63: sinmu = sin(mu*t0)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":63
* elam = exp(lam*t0)
* cosmu = cos(mu*t0)
* sinmu = sin(mu*t0) # <<<<<<<<<<<<<<
* y1t0 = elam*cosmu
* y1difft0 = elam*(lam*cosmu-mu*sinmu)
*/
__pyx_v_sinmu = sin((__pyx_v_mu * __pyx_v_t0));
64: y1t0 = elam*cosmu
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":64
* cosmu = cos(mu*t0)
* sinmu = sin(mu*t0)
* y1t0 = elam*cosmu # <<<<<<<<<<<<<<
* y1difft0 = elam*(lam*cosmu-mu*sinmu)
* y2t0 = elam*sinmu
*/
__pyx_v_y1t0 = (__pyx_v_elam * __pyx_v_cosmu);
65: y1difft0 = elam*(lam*cosmu-mu*sinmu)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":65
* sinmu = sin(mu*t0)
* y1t0 = elam*cosmu
* y1difft0 = elam*(lam*cosmu-mu*sinmu) # <<<<<<<<<<<<<<
* y2t0 = elam*sinmu
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*/
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66: y2t0 = elam*sinmu
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":66
* y1t0 = elam*cosmu
* y1difft0 = elam*(lam*cosmu-mu*sinmu)
* y2t0 = elam*sinmu # <<<<<<<<<<<<<<
* y2difft0 = elam*(lam*sinmu+mu*cosmu)
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*/
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67: y2difft0 = elam*(lam*sinmu+mu*cosmu)
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":67
* y1difft0 = elam*(lam*cosmu-mu*sinmu)
* y2t0 = elam*sinmu
* y2difft0 = elam*(lam*sinmu+mu*cosmu) # <<<<<<<<<<<<<<
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68: denominator = y1t0*y2difft0 - y2t0*y1difft0
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":68
* y2t0 = elam*sinmu
* y2difft0 = elam*(lam*sinmu+mu*cosmu)
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69: c1 = (y0*y2difft0 - y0p*y2t0)/denominator
/* "_sagenb_servers_sage_notebook_sagenb_sagenb_home_jason3_4_code_sage5_spyx_0.pyx":69
* y2difft0 = elam*(lam*sinmu+mu*cosmu)
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* c1 = (y0*y2difft0 - y0p*y2t0)/denominator # <<<<<<<<<<<<<<
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70: c2 = (-y0*y1difft0 + y0p*y1t0)/denominator
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* denominator = y1t0*y2difft0 - y2t0*y1difft0
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71: result.append(c1)
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* c1 = (y0*y2difft0 - y0p*y2t0)/denominator
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72: result.append(c2)
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73: r = sqrt(c1*c1+c2*c2)
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74: delta = atan2(c2,c1)
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75: result.append(r)
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76: result.append(delta)
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77:
78: return result
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