Expression of type Conditional

from the theory of proveit.physics.quantum.algebra

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, ExprRange, Function, IndexedVar, Q, Variable, c, f, j, m, n
from proveit.linear_algebra import MatrixSpace
from proveit.logic import InSet
from proveit.numbers import Complex, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
expr = Conditional(InSet(Function(f, sub_expr2), MatrixSpace(field = Complex, rows = n, columns = m)), Function(Q, sub_expr2))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \in \mathbb{C}^{n \times m} \textrm{ if } Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 9
3	Literal
4	ExprTuple	6, 7
5	Variable
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Variable
9	ExprTuple	12
10	Literal
11	NamedExprs	field: 13 rows: 14 columns: 15
12	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
13	Literal
14	Variable
15	Variable
16	Lambda	parameter: 22 body: 19
17	Literal
18	Variable
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable