switch to rational numbers + add variable type matrix library

mat.h

@@ -0,0 +1,66 @@
+#ifndef MAT_H
+#define MAT_H
+
+#include <gmp.h>
+#include <malloc.h>
+
+#define LOOP(i,n) for(int i = 0; i < (n); i++)
+
+// library for matrix computations in variable rings (based on GMP types)
+
+/*
+  needed features:
+  x multiply matrices
+  - inverse
+  - pseudoinverse
+  x set
+  - eigenvalues
+ */
+
+#define NUMBER mpq_t
+#define INIT mpq_init
+#define CLEAR mpq_clear
+#define SET mpq_set
+#define SET_ZERO(x) mpq_set_ui(x,0,1)
+#define SET_ONE(x) mpq_set_ui(x,1,1)
+#define ADD mpq_add
+#define SUB mpq_sub
+#define MULTIPLY mpq_mul
+#define DIV mpq_div
+#define PRINT(x) gmp_printf("%Qd", x)
+
+#define M(m,i,j) ((m)->x[(i)+(m)->n*(j)])
+
+struct _mat{
+	int n;
+	NUMBER *x;
+} ;
+
+typedef struct _mat mat[1];
+
+typedef struct _mat_workspace {
+	mat tmp_mat;
+	NUMBER tmp_num;
+	NUMBER tmp_num2;
+} mat_workspace;
+
+mat_workspace *mat_workspace_init(int n);
+void mat_workspace_clear(mat_workspace *ws);
+void mat_init(mat m, int n);
+void mat_get(NUMBER out, mat m, int i, int j);
+void mat_set(mat m, int i, int j, NUMBER x);
+NUMBER *mat_ref(mat m, int i, int j);
+void mat_zero(mat m);
+void mat_identity(mat m);
+void mat_copy(mat to, mat from);
+void mat_clear(mat m);
+int mat_same(mat m1, mat m2);
+static void mat_multiply_outofplace(mat_workspace *ws, mat out, mat in1, mat in2);
+void mat_multiply(mat_workspace *ws, mat out, mat in1, mat in2);
+void mat_det(mat_workspace *ws, NUMBER out, mat in);
+static void mat_pseudoinverse_outofplace(mat_workspace *ws, mat out, mat in);
+void mat_pseudoinverse(mat_workspace *ws, mat out, mat in);
+void mat_trace(NUMBER out, mat in);
+void mat_print(mat in);
+
+#endif