Expression of type Equals

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 ExprRange, Function, IndexedVar, Q, Variable, beta, c, delta, f, gamma, j
from proveit.core_expr_types import Len
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
from proveit.numbers import five, one
from proveit.physics.quantum import bra_varphi

# 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 = Equals(Len(operands = [beta, gamma, delta, bra_varphi, VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, five)]))

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(\beta, \gamma, \delta, \langle \varphi \rvert, \sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~f\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right)| = |\left(1, 2, \ldots, 5\right)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10, 11, 12
6	Literal
7	ExprTuple	13
8	Variable
9	Variable
10	Variable
11	Operation	operator: 14 operand: 20
12	Operation	operator: 16 operand: 21
13	ExprRange	lambda_map: 18 start_index: 30 end_index: 19
14	Literal
15	ExprTuple	20
16	Literal
17	ExprTuple	21
18	Lambda	parameter: 35 body: 35
19	Literal
20	Variable
21	Lambda	parameters: 27 body: 22
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 27
24	Operation	operator: 26 operands: 27
25	Variable
26	Variable
27	ExprTuple	28
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable