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I would like to manipulate arbitrarily large real numbers, for example:

a = 10**25+.1
round(a) # expected: 10000000000000000000000000
sage: 10000000000000000905969664
a.is_integer() # expected: False
sage: True
a - 10**25 # expected: 0.1
sage: 0.000000000000000

What is the appropriate function to use?

Arithmetic with large real numbers I would like to manipulate arbitrarily large real numbers, for example: a = 10**25+.

Say I have a map M:

[0,1] -> .3

[1,2] -> 1.1

[-3,-3] -> .6

etc.

I want to make a scatter plot where the point at P has size M[P]. How do I do this? Presumably I use the point2d object, which takes a size parameter.

Plot points of different sizes Say I have a map M: [0,1] -> .3 [1,2] -> 1.1 [-3,-3] -> .6 etc. I want to m

Suppose I have an integer lattice $L\subset\mathbb{Z}^2$ generated by $v_1$ and $v_2$. How do I check if $(x,y)\in L$?

I can easily create the lattice:

from sage.modules.free_module_integer import IntegerLattice
v1 = [3,4]
v2 = [4,5]
M = [v1,v2]
IL = IntegerLattice(M)

but nowhere in the documentation can I find a command to check for inclusion. I would like a solution that generalizes to lattices of any rank.

How do you check if a lattice contains a coordinate? Suppose I have an integer lattice $L\subset\mathbb{Z}^2$ generated