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Expression of type Lambda

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, Lambda, n
from proveit.linear_algebra import MatrixSpace, Unitary
from proveit.logic import InSet, SubsetEq
from proveit.numbers import Complex, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(SubsetEq(Unitary(n), MatrixSpace(field = Complex, rows = n, columns = n)), 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())
n \mapsto \left\{\textrm{U}\left(n\right) \subseteq \mathbb{C}^{n \times n} \textrm{ if } n \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 16
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple16, 10
8Operationoperator: 11
operand: 16
9Operationoperator: 13
operands: 14
10Literal
11Literal
12ExprTuple16
13Literal
14NamedExprsfield: 15
rows: 16
columns: 16
15Literal
16Variable