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Add shifts and truncate methods for arb_poly and acb_poly
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‎src/flint/types/acb_poly.pyx‎

Lines changed: 89 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -314,6 +314,95 @@ cdef class acb_poly(flint_poly):
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return s
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return divmod(t, s)
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def truncate(self, slong n):
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r"""
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Notionally truncate the polynomial to have length ``n``. If
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``n`` is larger than the length of the input, then a copy of ``self`` is
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returned. If ``n`` is not positive, then the zero polynomial
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is returned.
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Effectively returns this polynomial :math:`\mod x^n`.
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>>> f = acb_poly([1,2,3])
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>>> f.truncate(3)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.truncate(2)
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2.00000000000000*x + 1.00000000000000
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>>> f.truncate(1)
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1.00000000000000
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>>> f.truncate(0)
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0
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>>> f.truncate(-1)
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0
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"""
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cdef acb_poly res
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res = acb_poly.__new__(acb_poly)
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length = acb_poly_length(self.val)
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if n <= 0: # return zero
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return res
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elif n > length: # do nothing
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acb_poly_set(res.val, self.val)
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else:
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acb_poly_set_trunc(res.val, self.val, n)
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return res
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def left_shift(self, slong n):
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"""
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Returns ``self`` shifted left by ``n`` coefficients by inserting
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zero coefficients. This is equivalent to multiplying the polynomial
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by x^n
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>>> f = acb_poly([1,2,3])
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>>> f.left_shift(0)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.left_shift(1)
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3.00000000000000*x^3 + 2.00000000000000*x^2 + 1.00000000000000*x
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>>> f.left_shift(4)
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3.00000000000000*x^6 + 2.00000000000000*x^5 + 1.00000000000000*x^4
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"""
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cdef acb_poly res
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res = acb_poly.__new__(acb_poly)
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if n < 0:
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raise ValueError("Value must be shifted by a non-negative integer")
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if n > 0:
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acb_poly_shift_left(res.val, self.val, n)
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else: # do nothing, just copy self
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acb_poly_set(res.val, self.val)
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return res
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def right_shift(self, slong n):
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"""
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Returns ``self`` shifted right by ``n`` coefficients.
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This is equivalent to the floor division of the polynomial
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by x^n
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>>> f = acb_poly([1,2,3])
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>>> f.right_shift(0)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.right_shift(1)
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3.00000000000000*x + 2.00000000000000
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>>> f.right_shift(4)
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0
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"""
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cdef acb_poly res
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res = acb_poly.__new__(acb_poly)
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if n < 0:
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raise ValueError("Value must be shifted by a non-negative integer")
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if n > 0:
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acb_poly_shift_right(res.val, self.val, n)
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else: # do nothing, just copy self
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acb_poly_set(res.val, self.val)
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return res
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def __pow__(acb_poly s, ulong exp, mod):
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if mod is not None:
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raise NotImplementedError("acb_poly modular exponentiation")

‎src/flint/types/arb_poly.pyx‎

Lines changed: 89 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -312,6 +312,95 @@ cdef class arb_poly(flint_poly):
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return s
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return divmod(t, s)
314314

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def truncate(self, slong n):
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r"""
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Notionally truncate the polynomial to have length ``n``. If
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``n`` is larger than the length of the input, then a copy of ``self`` is
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returned. If ``n`` is not positive, then the zero polynomial
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is returned.
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Effectively returns this polynomial :math:`\mod x^n`.
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>>> f = arb_poly([1,2,3])
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>>> f.truncate(3)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.truncate(2)
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2.00000000000000*x + 1.00000000000000
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>>> f.truncate(1)
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1.00000000000000
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>>> f.truncate(0)
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0
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>>> f.truncate(-1)
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0
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"""
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cdef arb_poly res
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res = arb_poly.__new__(arb_poly)
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length = arb_poly_length(self.val)
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if n <= 0: # return zero
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return res
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elif n > length: # do nothing
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arb_poly_set(res.val, self.val)
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else:
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arb_poly_set_trunc(res.val, self.val, n)
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return res
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def left_shift(self, slong n):
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"""
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Returns ``self`` shifted left by ``n`` coefficients by inserting
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zero coefficients. This is equivalent to multiplying the polynomial
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by x^n
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>>> f = arb_poly([1,2,3])
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>>> f.left_shift(0)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.left_shift(1)
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3.00000000000000*x^3 + 2.00000000000000*x^2 + 1.00000000000000*x
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>>> f.left_shift(4)
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3.00000000000000*x^6 + 2.00000000000000*x^5 + 1.00000000000000*x^4
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"""
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cdef arb_poly res
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res = arb_poly.__new__(arb_poly)
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if n < 0:
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raise ValueError("Value must be shifted by a non-negative integer")
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if n > 0:
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arb_poly_shift_left(res.val, self.val, n)
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else: # do nothing, just copy self
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arb_poly_set(res.val, self.val)
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return res
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def right_shift(self, slong n):
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"""
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Returns ``self`` shifted right by ``n`` coefficients.
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This is equivalent to the floor division of the polynomial
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by x^n
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>>> f = arb_poly([1,2,3])
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>>> f.right_shift(0)
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3.00000000000000*x^2 + 2.00000000000000*x + 1.00000000000000
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>>> f.right_shift(1)
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3.00000000000000*x + 2.00000000000000
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>>> f.right_shift(4)
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0
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"""
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cdef arb_poly res
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res = arb_poly.__new__(arb_poly)
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if n < 0:
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raise ValueError("Value must be shifted by a non-negative integer")
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if n > 0:
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arb_poly_shift_right(res.val, self.val, n)
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else: # do nothing, just copy self
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arb_poly_set(res.val, self.val)
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return res
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def __pow__(arb_poly s, ulong exp, mod):
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if mod is not None:
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raise NotImplementedError("arb_poly modular exponentiation")

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