Revise initialization of generic algebraic curves

[sagetrac-gjorgenson]

Revise the Curve function used for initializing generic algebraic curves to allow passing an ambient space in which to construct the curve. Also modify how the curve function works when passing in a subscheme so the ambient space of that subscheme is used instead of creating a new one.

Additionally, implement curve functions for affine/projective space for initializing curves in those ambient spaces.

CC: @bhutz @miguelmarco

Component: algebraic geometry

Keywords: gsoc2016

Author: Grayson Jorgenson

Branch: d4eb8d4

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/20698

[sagetrac-gjorgenson]

Branch: u/gjorgenson/ticket/20698

[sagetrac-git]

Commit: 9cbdab3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9cbdab3

20698: revised initialization of generic curves.

[bhutz]

comment:4

Just a couple things here:

In the docs

• doc build error

OSError: [plane_cur] /home/ben/sage/sage-dev/local/lib/python2.7/site-packages/sage/schemes/plane_curves/constructor.py:docstring of sage.schemes.plane_curves.constructor.Curve:16: ERROR: Unexpected indentation.

• also variables names should be in double quote, single quote are for math type setting

also some issues with the error messsages

• Your raise is failing

A.<x,y,z> = ProjectiveSpace(QQ,2)
X=A.subscheme([x^3 + y^3 + z^3,x-y])
C = Curve(X);C

• the line wrap messed up the spacing

A.<x,y,z> = AffineSpace(QQ,3)
A2.<u,v,w,t>=AffineSpace(QQ,4)
C = Curve(x^3 + y^3 + z^3,A2);C

I didn't encounter any functionality issues.

[bhutz]

Reviewer: Ben Hutz

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b718afa

20698: documentation and error formatting fixes.

[sagetrac-git]

Changed commit from 9cbdab3 to b718afa

[sagetrac-gjorgenson]

comment:6

Thanks, the issues should be resolved now.

[bhutz]

comment:7

well, the docs compile, but the formatting isn't right.

• affine_space/curve
• projective_space/curve
• constructor/curve

take a look at the inputs.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d4eb8d4

20698: documentation spacing fixes.

[sagetrac-git]

Changed commit from b718afa to d4eb8d4

[sagetrac-gjorgenson]

comment:9

Oops, sorry. I changed the spacing and indentation, and the docs look better now.

[vbraun]

Changed branch from u/gjorgenson/ticket/20698 to d4eb8d4

[bhutz]

Changed keywords from none to gsoc2016

[bhutz]

Changed commit from d4eb8d4 to none