Zabm

cypari2/gen.pyx

@@ -3213,6 +3213,62 @@ cdef class Gen(Gen_base):
             raise ValueError("%s is not a square modulo %s" % (self, n))
         return new_gen(s)
 
+    def ZabM_ker(self, Gen P, long n):
+        r"""
+        Return an integral primitive basis of the kernel of this matrix.
+
+        INPUT:
+
+        - ``P`` - cyclotomic polynomial
+
+        - ``n`` - order of the cyclotomic polynomial
+
+        Examples:
+
+        >>> from cypari2 import Pari
+        >>> pari = Pari()
+
+        >>> x = pari('x')
+        >>> M = pari([[2*x + 5, x - 4], [-2*x**2 - 5*x, -x**2 + 4*x]])
+        >>> M.ZabM_ker(pari.polcyclo(5), 5)
+        [x; 1]
+        """
+        cdef GEN s
+        sig_on()
+        s = ZabM_ker(self.g, P.g, n)
+        return new_gen(s)
+
+    def ZabM_indexrank(self, Gen P, long n):
+        r"""
+        Return a vector with two t_VECSMALL components giving the rank profile of this
+        matrix.
+
+        Inefficient (but correct) when the matrix does not have almost full column rank.
+
+        INPUT:
+
+        - ``P`` - cyclotomic polynomial
+
+        - ``n`` - order of the cyclotomic polynomial
+
+        Examples:
+
+        >>> from cypari2 import Pari
+        >>> pari = Pari()
+
+        >>> x = pari('x')
+        >>> M = pari([[2*x + 5, x - 4], [-2*x**2 - 5*x, -x**2 + 4*x]])
+        >>> M.ZabM_indexrank(pari.polcyclo(5), 5)
+        [Vecsmall([1]), Vecsmall([1])]
+        >>> M = pari([[2*x + 5, x - 3], [-2*x**2 - 5*x, -x**2 + 4*x]])
+        >>> M.ZabM_indexrank(pari.polcyclo(5), 5)
+        [Vecsmall([1, 2]), Vecsmall([1, 2])]
+        """
+        cdef GEN s
+        sig_on()
+        s = ZabM_indexrank(self.g, P.g, n)
+        return new_gen(s)
+
     def ellan(self, long n, python_ints=False):
         """
         Return the first `n` Fourier coefficients of the modular

cypari2/paridecl.pxd

@@ -771,16 +771,19 @@ cdef extern from *:     # PARI headers already included by types.pxd
     GEN     F2m_F2c_mul(GEN x, GEN y)
     GEN     F2m_mul(GEN x, GEN y)
     GEN     F2m_powu(GEN x, ulong n)
+    GEN     Flc_Flv_mul(GEN x, GEN y, ulong p)
     GEN     Flc_to_mod(GEN z, ulong pp)
     GEN     Flm_Fl_add(GEN x, ulong y, ulong p)
     GEN     Flm_Fl_mul(GEN y, ulong x, ulong p)
     void    Flm_Fl_mul_inplace(GEN y, ulong x, ulong p)
     GEN     Flm_Flc_mul(GEN x, GEN y, ulong p)
     GEN     Flm_Flc_mul_pre(GEN x, GEN y, ulong p, ulong pi)
+    GEN     Flm_Flc_mul_pre_Flx(GEN x, GEN y, ulong p, ulong pi, long sv)
     GEN     Flm_add(GEN x, GEN y, ulong p)
     GEN     Flm_center(GEN z, ulong p, ulong ps2)
     GEN     Flm_mul(GEN x, GEN y, ulong p)
     GEN     Flm_neg(GEN y, ulong p)
+    GEN     Flm_powers(GEN x, ulong n, ulong p)
     GEN     Flm_powu(GEN x, ulong n, ulong p)
     GEN     Flm_sub(GEN x, GEN y, ulong p)
     GEN     Flm_to_mod(GEN z, ulong pp)
@@ -834,6 +837,11 @@ cdef extern from *:     # PARI headers already included by types.pxd
     GEN     FpV_to_mod(GEN z, GEN p)
     GEN     FpVV_to_mod(GEN z, GEN p)
     GEN     FpX_to_mod(GEN z, GEN p)
+    GEN     ZabM_ker(GEN M, GEN P, long n)
+    GEN     ZabM_indexrank(GEN M, GEN P, long n)
+    GEN     ZabM_inv(GEN M, GEN P, long n, GEN *pden)
+    GEN     ZabM_inv_ratlift(GEN M, GEN P, long n, GEN *pden)
+    GEN     ZabM_pseudoinv(GEN M, GEN P, long n, GEN *pv, GEN *den)
     GEN     ZV_zMs_mul(GEN B, GEN M)
     GEN     ZpMs_ZpCs_solve(GEN M, GEN B, long nbrow, GEN p, long e)
     GEN     gen_FpM_Wiedemann(void *E, GEN (*f)(void*, GEN), GEN B, GEN p)
@@ -843,6 +851,9 @@ cdef extern from *:     # PARI headers already included by types.pxd
     GEN     matid_Flm(long n)
     GEN     matid_F2xqM(long n, GEN T)
     GEN     matid_FlxqM(long n, GEN T, ulong p)
+    GEN     random_Flv(long n, ulong p)
+    GEN     random_FpC(long d, GEN p)
+    GEN     random_FpV(long d, GEN p)
     GEN     scalar_Flm(long s, long n)
     GEN     zCs_to_ZC(GEN C, long nbrow)
     GEN     zMs_to_ZM(GEN M, long nbrow)