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Expression of type ExprTuple

from the theory of proveit.linear_algebra.matrices

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, m, n
from proveit.linear_algebra import MatrixSpace, VecSpaces
from proveit.logic import And, InClass, InSet
from proveit.numbers import Complex, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(InClass(MatrixSpace(field = Complex, rows = m, columns = n), VecSpaces(Complex)), And(InSet(m, NaturalPos), InSet(n, NaturalPos)))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(m, n\right) \mapsto \left\{\mathbb{C}^{m \times n} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(\mathbb{C}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple22, 23
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10Operationoperator: 14
operands: 15
11Operationoperator: 16
operand: 21
12Operationoperator: 19
operands: 18
13Operationoperator: 19
operands: 20
14Literal
15NamedExprsfield: 21
rows: 22
columns: 23
16Literal
17ExprTuple21
18ExprTuple22, 24
19Literal
20ExprTuple23, 24
21Literal
22Variable
23Variable
24Literal