Opened 6 years ago

## #18419 new enhancement

# Extend truncation of polynomials and harmonize with __getitem__

Reported by: | vdelecroix | Owned by: | |
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Priority: | major | Milestone: | sage-6.7 |

Component: | algebra | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

The current `truncate`

methods of polynomials is

cpdef truncate(self, n): r""" return self modulo X^n """

In many algorithms it is desirable to have a more general truncation

cpdef truncate(self, l, h): r""" Given a polynomial p = a_0 + a_1 X + ... + a_d X^d return the polynomial a_l + a_{l+1} X + ... + a_{h-1] X^h """

It would be the very same semantic than for the `__getitem__`

.

sage: R.<x> = QQ[] sage: p = 0 + 1*x + 2*x^2 + 3*x^3 + 4*x^4 sage: p[1:3] 2*x^2 + x sage: p[2:] 4*x^4 + 3*x^3 + 2*x^2

Currently the `__getitem__`

method is a generic one. But for slices of the form `(a,b,1)`

we should rely on `truncate`

that can be optimized in derived classes.

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