Added fmpz_mod_mpoly_q module

CMakeLists.txt

@@ -238,7 +238,7 @@ set(_BUILD_DIRS
     nmod_poly_mat                   fmpz_poly_mat
 
     mpoly           nmod_mpoly      fmpz_mpoly      fmpz_mod_mpoly
-    fmpq_mpoly      fq_nmod_mpoly   fq_zech_mpoly
+    fmpq_mpoly      fq_nmod_mpoly   fq_zech_mpoly   fmpz_mod_mpoly_q
 
     nmod_mpoly_factor               fmpz_mpoly_factor
     fmpz_mod_mpoly_factor           fmpq_mpoly_factor

Makefile.in

@@ -187,7 +187,7 @@ HEADER_DIRS :=                                                              \
         nmod_poly_mat                   fmpz_poly_mat                       \
                                                                             \
         mpoly           nmod_mpoly      fmpz_mpoly      fmpz_mod_mpoly      \
-        fmpq_mpoly      fq_nmod_mpoly   fq_zech_mpoly                       \
+        fmpq_mpoly      fq_nmod_mpoly   fq_zech_mpoly   fmpz_mod_mpoly_q    \
                                                                             \
         nmod_mpoly_factor               fmpz_mpoly_factor                   \
         fmpz_mod_mpoly_factor           fmpq_mpoly_factor                   \

doc/source/fmpz_mod_mpoly_q.rst

@@ -0,0 +1,212 @@
+.. _fmpz-mpoly-q:
+
+**fmpz_mod_mpoly_q.h** -- multivariate rational functions over Q
+===============================================================================
+
+An :type:`fmpz_mod_mpoly_q_t` represents an element of 
+`\mathbb{F}_m(x_1,\ldots,x_n)` for some prime number *m* and fixed *n* as a pair of FLINT 
+multivariate polynomials (:type:`fmpz_mod_mpoly_t`).
+Instances are always kept in canonical form by ensuring that the GCD
+of numerator and denominator is 1 and then normalizing denominator to a monic polynomial.
+
+The user must create a multivariate polynomial context
+(:type:`fmpz_mod_mpoly_ctx_t`) specifying the prime number *m* for the field `\mathbb{F}_m` 
+the number of variables *n* and the monomial ordering.
+
+
+Types and macros
+-------------------------------------------------------------------------------
+
+.. type:: fmpz_mod_mpoly_q_struct
+
+.. type:: fmpz_mod_mpoly_q_t
+
+    An *fmpz_mod_mpoly_q_struct* consists of a pair of *fmpz_mod_mpoly_struct*:s.
+    An *fmpz_mod_mpoly_q_t* is defined as an array of length one of type
+    *fmpz_mod_mpoly_q_struct*, permitting an *fmpz_mod_mpoly_q_t* to be passed by
+    reference.
+
+.. macro:: fmpz_mod_mpoly_q_numref(x)
+
+    Macro returning a pointer to the numerator of *x* which can be used as an *fmpz_mod_mpoly_t*.
+
+.. macro:: fmpz_mod_mpoly_q_denref(x)
+
+    Macro returning a pointer to the denominator of *x* which can be used as an *fmpz_mod_mpoly_t*.
+
+
+Memory management
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_init(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Initializes *res* for use, and sets its value to zero.
+
+.. function:: void fmpz_mod_mpoly_q_clear(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Clears *res*, freeing or recycling its allocated memory.
+
+
+Assignment
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_swap(fmpz_mod_mpoly_q_t x, fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Swaps the values of *x* and *y* efficiently.
+
+.. function:: void fmpz_mod_mpoly_q_set(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_set_fmpq(fmpz_mod_mpoly_q_t res, const fmpq_t x, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_set_fmpz(fmpz_mod_mpoly_q_t res, const fmpz_t x, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_set_si(fmpz_mod_mpoly_q_t res, slong x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the value *x*.
+
+
+Canonicalisation
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_canonicalise(fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Puts the numerator and denominator of *x* in canonical form by removing
+    common content and making the denominator monic.
+
+.. function:: int fmpz_mod_mpoly_q_is_canonical(const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Returns whether *x* is in canonical form.
+
+    In addition to verifying that the numerator and denominator
+    have no common content and that the denominator 
+    is monic, this function checks that the denominator is nonzero and that
+    the numerator and denominator have correctly sorted terms
+    (these properties should normally hold; verifying them
+    provides an extra consistency check for test code).
+
+Properties
+-------------------------------------------------------------------------------
+
+.. function:: int fmpz_mod_mpoly_q_is_zero(const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Returns whether *x* is the constant 0.
+
+.. function:: int fmpz_mod_mpoly_q_is_one(const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Returns whether *x* is the constant 1.
+
+.. function:: void fmpz_mod_mpoly_q_used_vars(int * used, const fmpz_mod_mpoly_q_t f, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_used_vars_num(int * used, const fmpz_mod_mpoly_q_t f, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_used_vars_den(int * used, const fmpz_mod_mpoly_q_t f, const fmpz_mod_mpoly_ctx_t ctx)
+
+    For each variable, sets the corresponding entry in *used* to the
+    boolean flag indicating whether that variable appears in the
+    rational function (respectively its numerator or denominator).
+
+Special values
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_zero(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the constant 0.
+
+.. function:: void fmpz_mod_mpoly_q_one(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the constant 1.
+
+.. function:: void fmpz_mod_mpoly_q_gen(fmpz_mod_mpoly_q_t res, slong i, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the generator `x_{i+1}`.
+    Requires `0 \le i < n` where *n* is the number of variables of *ctx*.
+
+
+Input and output
+-------------------------------------------------------------------------------
+
+The variable strings in *x* start with the variable of most significance at index `0`. If *x* is ``NULL``, the variables are named ``x1``, ``x2``, etc.
+
+.. function:: void fmpz_mod_mpoly_q_print_pretty(const fmpz_mod_mpoly_q_t f, const char ** x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Prints *res* to standard output. If *x* is not *NULL*, the strings in
+    *x* are used as the symbols for the variables.
+
+.. function:: char * fmpz_mod_mpoly_q_get_str_pretty(const fmpz_mod_mpoly_q_t f, const char ** x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Return a string, which the user is responsible for cleaning up, representing *f*, given an array of variable strings *x*.
+
+.. function:: int fmpz_mod_mpoly_q_set_str_pretty(fmpz_mod_mpoly_q_t res, const char * s, const char ** x, fmpz_mod_mpoly_ctx_t ctx)
+
+    Set *res* to the fraction in the null-terminated string *str* given an array *x* of variable strings.
+    If parsing *str* fails, *res* is set to zero, and `-1` is returned. Otherwise, `0` is returned.
+    The operations ``+``, ``-``, ``*``, and ``/`` are permitted along with integers and the variables in *x*.
+    The character ``^`` must be immediately followed by the (integer) exponent.
+    If division by zero occurs, parsing fails.
+
+Random generation
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_randtest(fmpz_mod_mpoly_q_t res, flint_rand_t state, slong length, slong exp_bound, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to a random rational function where both numerator and denominator
+    have up to *length* terms and exponents strictly smaller than *exp_bound*.
+
+
+Comparisons
+-------------------------------------------------------------------------------
+
+.. function:: int fmpz_mod_mpoly_q_equal(const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Returns whether *x* and *y* are equal.
+
+
+Arithmetic
+-------------------------------------------------------------------------------
+
+.. function:: void fmpz_mod_mpoly_q_neg(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the negation of *x*.
+
+.. function:: void fmpz_mod_mpoly_q_add(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_add_fmpq(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpq_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_add_fmpz(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_add_si(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, slong y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the sum of *x* and *y*.
+
+.. function:: void fmpz_mod_mpoly_q_sub(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_sub_fmpq(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpq_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_sub_fmpz(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_sub_si(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, slong y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the difference of *x* and *y*.
+
+.. function:: void fmpz_mod_mpoly_q_mul(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_mul_fmpq(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpq_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_mul_fmpz(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_mul_si(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, slong y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the product of *x* and *y*.
+
+.. function:: void fmpz_mod_mpoly_q_div(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_q_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_div_fmpq(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpq_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_div_fmpz(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_t y, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_div_si(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, slong y, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the quotient of *x* and *y*.
+    Division by zero calls *flint_abort*.
+
+.. function:: void fmpz_mod_mpoly_q_inv(fmpz_mod_mpoly_q_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the inverse of *x*. Division by zero
+    calls *flint_abort*.
+
+Content
+-------------------------------------------------------------------------------
+
+.. function:: void _fmpz_mod_mpoly_q_content(fmpz_t num, fmpz_t den, const fmpz_mod_mpoly_t xnum, const fmpz_mod_mpoly_t xden, const fmpz_mod_mpoly_ctx_t ctx)
+              void fmpz_mod_mpoly_q_content(fmpq_t res, const fmpz_mod_mpoly_q_t x, const fmpz_mod_mpoly_ctx_t ctx)
+
+    Sets *res* to the content of the coefficients of *x*.
+
+
+.. raw:: latex
+
+    \newpage
+