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// Copyright 2013 Michael E. Stillman
#ifndef __ring_test_hpp__
#define __ring_test_hpp__
#include <cstdio>
#include <string>
#include <iostream>
//#include <sstream>
#include <memory>
#include <gtest/gtest.h>
//#include <mpfr.h>
#include "interface/random.h"
#include "ZZ.hpp"
#include "exceptions.hpp"
const int ntrials = 100; // 5000
template <typename T>
std::istream& fromStream(std::istream& i,
const T& R,
typename T::ElementType& result);
template <typename T>
bool fromStream(std::istream& i, const T& R, ring_elem& result);
template <typename T>
std::string ringName(const T& R)
{
buffer o;
R.text_out(o);
std::string result = o.str();
return result;
}
template <typename RingType>
ring_elem getElement(const RingType& R, int index);
template <typename RingType>
class RingElementGenerator
{
public:
RingElementGenerator(const RingType& R) : mRing(R), mNext(0) {}
ring_elem nextElement() { return getElement<RingType>(mRing, ++mNext); }
void reset() { mNext = 0; }
private:
const RingType& mRing;
int mNext;
};
template <typename T>
void testRingCoercions(const T* R, int ntrials)
{
// from int
// from mpz
// from rational
}
template <typename T>
void testRingNegate(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
// test: (-a) + (a) == a
ring_elem a = gen.nextElement();
ring_elem b = R->negate(a);
ring_elem c = R->add(a, b);
EXPECT_TRUE(R->is_zero(c));
}
}
template <typename T>
void testRingAdd(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
// test: (a+b) + (-b) == a
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
ring_elem c = R->add(a, b);
ring_elem d = R->negate(b);
ring_elem e = R->add(c, d); // should be a
EXPECT_TRUE(R->is_equal(e, a));
}
}
template <typename T>
void testRingSubtract(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
// test: (a-b) + (b) == a
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
ring_elem c = R->subtract(a, b);
ring_elem e = R->add(c, b);
EXPECT_TRUE(R->is_equal(e, a));
}
}
template <typename T>
void testRingDivide(const T* R, int ntrials)
{
auto zero = R->zero();
auto a = R->from_long(3);
EXPECT_ANY_THROW(R->divide(a, zero));
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
// test: (a*b) // b == a
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
ring_elem c = R->mult(a, b);
if (R->is_zero(b))
EXPECT_TRUE(R->is_zero(c));
else
{
ring_elem d = R->divide(c, b);
EXPECT_TRUE(R->is_equal(d, a));
}
}
}
template <typename T>
void testRingAxioms(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
ring_elem c = gen.nextElement();
// Test commutativity
// test: a*b = b*a
// test: a+b == b+a
ring_elem d = R->add(a, b);
ring_elem e = R->add(b, a);
EXPECT_TRUE(R->is_equal(d, e));
d = R->mult(a, b);
e = R->mult(b, a);
EXPECT_TRUE(R->is_equal(d, e));
// Test associativity
// test: a+(b+c) == (a+b)+c
// test: a*(b*c) == (a*b)*c
d = R->add(a, R->add(b, c));
e = R->add(R->add(a, b), c);
EXPECT_TRUE(R->is_equal(d, e));
d = R->mult(a, R->mult(b, c));
e = R->mult(R->mult(a, b), c);
EXPECT_TRUE(R->is_equal(d, e));
// Test distributivity
// test: a*(b+c) == a*b + a*c
d = R->mult(a, R->add(b, c));
e = R->add(R->mult(a, b), R->mult(a, c));
EXPECT_TRUE(R->is_equal(d, e));
}
}
template <typename T>
void testRingPower(const T* R, int ntrials)
{
mpz_t gmp1;
mpz_init(gmp1);
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
ring_elem a = gen.nextElement();
// TODO: what should the answer here be?
// EXPECT_TRUE(R->is_equal(R->power(a, 0), R->one())); // 0^0 == 1 too?
EXPECT_TRUE(R->is_equal(R->power(a, 1), a));
int e1 = rawRandomInt(10) + 1;
int e2 = rawRandomInt(10) + 1;
// std::cout << "(" << e1 << "," << e2 << ")" << std::endl;
ring_elem b = R->power(a, e1);
ring_elem c = R->power(a, e2);
ring_elem d = R->power(a, e1 + e2);
EXPECT_TRUE(R->is_equal(R->mult(b, c), d));
// Make sure that powers via mpz work (at least for small exponents)
mpz_set_si(gmp1, e1);
ring_elem b1 = R->power(a, gmp1);
EXPECT_TRUE(R->is_equal(b1, b));
}
mpz_clear(gmp1);
}
template <typename T>
void testRingGCD(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
// (a // gcd(a,b) == 0, b // gcd(a,b) == 0,
ring_elem c = R->gcd(a, b);
ring_elem u, v;
ring_elem d = R->gcd_extended(a, b, u, v);
EXPECT_TRUE(R->is_equal(c, d));
EXPECT_TRUE(R->is_equal(c, R->add(R->mult(a, u), R->mult(b, v))));
EXPECT_TRUE(R->is_equal(a, R->mult(R->divide(a, c), c)));
}
}
template <typename T>
void testRingRemainder(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
#if 0
ring_elem c = R->remainder(a, R->zero()); // FAILS!!
EXPECT_TRUE(R->is_equal(c,a));
#endif
ring_elem r = R->remainder(a, b);
ring_elem q = R->quotient(a, b);
ring_elem r1, q1;
r1 = R->remainderAndQuotient(a, b, q1);
EXPECT_TRUE(R->is_equal(r, r1));
EXPECT_TRUE(R->is_equal(q, q1));
ring_elem a1 = R->add(R->mult(q, b), r);
EXPECT_TRUE(R->is_equal(a, a1));
}
}
template <typename T>
void testRingSyzygy(const T* R, int ntrials)
{
RingElementGenerator<T> gen(*R);
for (int i = 0; i < ntrials; i++)
{
ring_elem u, v;
ring_elem a = gen.nextElement();
ring_elem b = gen.nextElement();
if (R->is_zero(b)) continue;
// special cases (note: b != 0 for rest of routine)
// syzygy(0,b) returns (1,0)
R->syzygy(R->zero(), b, u, v);
EXPECT_TRUE(R->is_equal(u, R->one()));
EXPECT_TRUE(R->is_equal(v, R->zero()));
// syzygy(a,1) returns (1,-a)
R->syzygy(a, R->one(), u, v);
EXPECT_TRUE(R->is_equal(u, R->one()));
EXPECT_TRUE(R->is_equal(v, R->negate(a)));
// syzygy(a,-1) returns (1,a)
R->syzygy(a, R->minus_one(), u, v);
EXPECT_TRUE(R->is_equal(u, R->one()));
EXPECT_TRUE(R->is_equal(v, a));
R->syzygy(a, b, u, v);
ring_elem result = R->add(R->mult(a, u), R->mult(b, v));
#if 0
buffer o;
o << "a=";
R->elem_text_out(o,a);
o << " b=";
R->elem_text_out(o,b);
o << " u=";
R->elem_text_out(o,u);
o << " v=";
R->elem_text_out(o,v);
std::cout << o.str() << std::endl;
#endif
EXPECT_TRUE(R->is_zero(result));
}
// over ZZ:
// syzygy(a,b) returns (b/c, -a/c), where c = +- gcd(a,b), with same sign as b
}
#endif
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e/unit-tests check "
// indent-tabs-mode: nil
// End:
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