padic_mat.h

Returns a pointer to the integer matrix $M$, for use with the functions of fmpz_mat.h.

Returns a pointer to the entry $(i, j)$ of $M$, which is not necessarily a unit.

Return the valuation $v$ and the precision $N$ of $A$.

Return the number of rows and columns of $A$.

Initialise $A$ as the zero matrix with $r$ rows and $c$ columns and precision PADIC_DEFAULT_PREC (that is, 20), respectively prec.

Clears $A$.

Brings $A$ into canonical form by dividing $M$ by the largest power of $p$ dividing all entries; sets $v = 0$ if $M = 0$. No reduction.

Reduces the canonical matrix $A$ modulo $p^N$, setting it to zero if $v \ge N$.

Canonicalises and reduces $A$.

Return whether $A$ has zero rows or zero columns, respectively as many rows as columns.

Returns whether $A$ is in canonical form.

Returns whether $A$ is reduced: empty, or zero with $v = 0$, or canonical with $v < N$ and all entries less than $p^{N - v}$. The entries are not checked to be nonnegative.

Sets $B$ to $A$, reduced to the precision of $B$.

Swaps $A$ and $B$, including dimensions, valuations and precisions, in constant time.

Swaps the entries of the integer matrices of mat1 and mat2, which must have the same dimensions, one by one. The valuations and precisions are not swapped, so the result is meaningful only if they agree.

Sets $A$ to the zero matrix.

Sets the square matrix $A$ to the identity matrix, or to zero if its precision is not positive.

Sets $B$ to the rational matrix $A$, reduced to the precision of $B$. The valuation of $B$ is the minimum valuation of the entries of $A$.

Sets the rational matrix $B$ to $p^v M$.

Sets rop to the entry $(i, j)$, that is, to $p^v M_{ij}$ reduced to the precision of rop.

Sets the entry $(i, j)$ of rop to op and restores canonical form. If op has smaller valuation than rop, all entries are multiplied by a power of $p$. The value is not reduced to the precision of rop; call padic_mat_reduce afterwards if op may have a higher precision than rop.

Returns whether the stored values are equal, that is, whether the valuations and the integer matrices agree. The matrices must be canonical; the precisions are not compared.

Returns whether $A$ is the zero matrix (with $v = 0$).

Print the number of rows, a space, the number of columns, two spaces and the entries row by row, separated by spaces. In the mode PADIC_TERSE the entries are printed as rationals, in PADIC_VAL_UNIT in the form p^w*u; the mode PADIC_SERIES is not supported and throws. Return 1.

Print $A$ as a list of rows in square brackets, one row per line, each entry in the printing mode of the context. Return 1.

Sets $A$ to a random reduced matrix, with valuation drawn as for padic_randtest.

Sets $B$ to the transpose of $A$. The precision of $B$ is not applied. Aliasing is allowed for square matrices.

Sets $C$ to $A + B$, reduced, for nonempty matrices with $\operatorname{ord}_p(A) \ge \operatorname{ord}_p(B)$, which is not checked.

Sets $C$ to $A + B$, reduced.

Sets $C$ to $A - B$ in canonical form, for nonempty matrices. The result is not reduced in general.

Sets $C$ to $A - B$, reduced.

Sets $B$ to $-A$ in canonical form; the entries are negated and not reduced.

Sets $B$ to $-A$, reduced.

Set $B$ to $cA$ in canonical form, without reduction. For an integer $c$ its power of $p$ is moved into the valuation.

Set $B$ to $cA$, reduced.

Sets $B$ to $A/c$, reduced. The power of $p$ in $c$ is subtracted from the valuation and the rest of $c$ is inverted modulo $p^{N - v}$. Throws if $c = 0$.

Sets $C$ to $AB$, reduced. The integer matrices are multiplied with fmpz_mat_mul (Multiplying matrices over the integers), the valuations are added, and the product is canonicalised and reduced: unlike for polynomials, the product of two canonical matrices may be divisible by $p$. Allows aliasing.