#!/usr/bin/env python3

from linpy import *


class Transformer:

    def __new__(cls, polyhedron, range_symbols, domain_symbols):
        self = object().__new__(cls)
        self.polyhedron = polyhedron
        self.range_symbols = range_symbols
        self.domain_symbols = domain_symbols
        return self

    @property
    def symbols(self):
        return self.range_symbols + self.domain_symbols

    def star(self):
        delta_symbols = [symbol.asdummy() for symbol in self.range_symbols]
        k = Dummy('k')
        polyhedron = self.polyhedron
        for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
            polyhedron &= Eq(dx, xprime - x)
        polyhedron = polyhedron.project(self.symbols)
        equalities, inequalities = [], []
        for equality in polyhedron.equalities:
            equality += (k-1) * equality.constant
            equalities.append(equality)
        for inequality in polyhedron.inequalities:
            inequality += (k-1) * inequality.constant
            inequalities.append(inequality)
        polyhedron = Polyhedron(equalities, inequalities) & Ge(k, 0)
        polyhedron = polyhedron.project([k])
        for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
            polyhedron &= Eq(dx, xprime - x)
        polyhedron = polyhedron.project(delta_symbols)
        return Transformer(polyhedron, self.range_symbols, self.domain_symbols)


if __name__ == '__main__':
    i, iprime, j, jprime = symbols("i i' j j'")
    transformer = Transformer(Eq(iprime, i + 2) & Eq(jprime, j + 1),
        [i, j], [iprime, jprime])
    print('T  =', transformer.polyhedron)
    print('T* =', transformer.star().polyhedron)