#include <stdlib.h>
#include <polylib/polylib.h>
Go to the source code of this file.
Functions | |
void | moins_l (Value *a, int i, int n, int p) |
void | moins_c (Value *a, int i, int n, int p) |
void | echange_l (Value *a, int i, int j, int n, int p) |
void | echange_c (Value *a, int i, int j, int n, int p) |
void | ligne (Value *a, int i, int j, Value x, int n, int p) |
void | colonne (Value *a, int i, int j, Value x, int n, int p) |
int | petit_l (Value *a, int n, int p, int q) |
int | petit_c (Value *a, int n, int p, int q) |
void | identite (Value *a, int n, int p) |
void | transpose (Value *a, int n, int q) |
int | encore (Value *a, int n, int p, int q, Value val) |
void | smith (Value *a, Value *b, Value *c, Value *b_inverse, Value *c_inverse, int n, int p, int q) |
void | hermite (Value *a, Value *b, Value *d, int n, int p, int q) |
Value * | ConvertPolMattoDarMat (Matrix *A) |
Convert PolmattoDarmat : This function converts the matrix of a Polylib to a int * as necessary for the functions in Darte's implementation. | |
Matrix * | ConvertDarMattoPolMat (Value *A, int NbRows, int NbCols) |
Convert DarmattoPolmat This function converts the matrix from Darte representation to a matrix in PolyLib. | |
void | Smith (Matrix *A, Matrix **U, Matrix **V, Matrix **Product) |
Smith : This function takes a Matrix A of dim n * l as its input and returns the three matrices U, V and Product such that A = U * Product * V, where U is an unimodular matrix of dimension n * n and V is an unimodular matrix of dimension l * l. | |
void | Hermite (Matrix *A, Matrix **H, Matrix **U) |
Hermite : This function takes a Matrix as its input and finds its HNF ( Left form ). |
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Definition at line 133 of file NormalForms.c. References Value, value_addto, value_clear, value_init, and value_multiply. |
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Convert DarmattoPolmat This function converts the matrix from Darte representation to a matrix in PolyLib. Input : The matrix (a pointer to it), number of Rows, number of columns Output : The matrix of the PolyLib Definition at line 595 of file NormalForms.c. References Matrix, Matrix_Alloc(), matrix::p, Value, and value_assign. |
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Convert PolmattoDarmat : This function converts the matrix of a Polylib to a int * as necessary for the functions in Darte's implementation. Input : A Polylib Matrix ( a pointer to it ); Output : An int * with the matrix copied into it Definition at line 571 of file NormalForms.c. References Matrix, matrix::NbColumns, matrix::NbRows, matrix::p, Value, value_assign, and value_init. |
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Definition at line 76 of file NormalForms.c. References s, Value, value_assign, value_clear, and value_init. |
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Definition at line 50 of file NormalForms.c. References s, Value, value_assign, value_clear, and value_init. |
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Definition at line 320 of file NormalForms.c. References Value, value_absolute, value_clear, value_init, value_modulus, value_notzero_p, and value_zero_p. Referenced by smith(). |
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Hermite : This function takes a Matrix as its input and finds its HNF ( Left form ). Input : A Matrix A (The Matrix A is not necessarily a Polylib matrix. It is just a matrix as far as Hermite is concerned. It does not even check if the matrix is a Polylib matrix or not) Output : The Hnf matrix H and the Unimodular matrix U such that A = H * U. We use Alan Darte's implementation of Hermite to compute the HNF. Alan Darte's implementation computes the Upper Triangular HNF. So We work on the fact that if A = H * U then A (transpose) = U(transpose) * H (transpose) There are a set of interface functions written in Interface.c which convert a matrix from Polylib representationt to that of Alan Darte's and vice versa. This Function Does the Following Step 1 : Given the matrix A it finds its Transpose. Step 2 : Finds the HNF (Right Form) using Alan Darte's Algorithm. Step 3 : The H1 and U1 obtained in Step2 are both Transposed to get the actual H and U such that A = HU. Definition at line 695 of file NormalForms.c. References ConvertDarMattoPolMat(), ConvertPolMattoDarMat(), hermite(), identite(), Matrix, Matrix_Copy(), Matrix_Free(), matrix::NbColumns, matrix::NbRows, Transpose(), transpose(), Value, value_clear, and value_init. |
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Definition at line 483 of file NormalForms.c. References colonne(), echange_c(), echange_l(), ligne(), moins_c(), moins_l(), petit_c(), Value, value_assign, value_clear, value_decrement, value_division, value_init, value_modulus, value_neg_p, value_notzero_p, and value_oppose. Referenced by Hermite(), left_hermite(), and right_hermite(). |
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Definition at line 263 of file NormalForms.c. References Value, and value_set_si. |
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Definition at line 104 of file NormalForms.c. References Value, value_addto, value_clear, value_init, and value_multiply. |
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Definition at line 31 of file NormalForms.c. References Value, and value_oppose. |
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Definition at line 12 of file NormalForms.c. References Value, and value_oppose. |
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Definition at line 216 of file NormalForms.c. References Value, value_absolute, value_assign, value_clear, value_ge, value_init, and value_notzero_p. |
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Definition at line 164 of file NormalForms.c. References Value, value_absolute, value_assign, value_clear, value_ge, value_init, and value_notzero_p. Referenced by smith(). |
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Smith : This function takes a Matrix A of dim n * l as its input and returns the three matrices U, V and Product such that A = U * Product * V, where U is an unimodular matrix of dimension n * n and V is an unimodular matrix of dimension l * l. Product is a diagonal matrix of dimension n * l. We use Alan Darte's implementation of Smith for computing the Smith Normal Form Definition at line 619 of file NormalForms.c. References ConvertDarMattoPolMat(), ConvertPolMattoDarMat(), identite(), Matrix, Matrix_Alloc(), Matrix_Free(), Matrix_Inverse(), matrix::NbColumns, matrix::NbRows, smith(), Value, value_clear, and value_init. |
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Definition at line 374 of file NormalForms.c. References colonne(), echange_c(), echange_l(), encore(), ligne(), moins_c(), moins_l(), petit_c(), petit_l(), Value, value_assign, value_clear, value_decrement, value_division, value_init, value_modulus, value_neg_p, value_notzero_p, value_oppose, and value_set_si. Referenced by Smith(). |
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Definition at line 288 of file NormalForms.c. References Value, value_assign, value_clear, and value_init. Referenced by Hermite(). |