Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, ExprTuple, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import MatrixExp
from proveit.numbers import Add, Exp, Neg, one, two, zero
from proveit.physics.quantum.QPE import _U

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [ExprRange(sub_expr1, MatrixExp(_U, Exp(two, Neg(sub_expr1))), Add(Neg(t), one), zero).with_decreasing_order()]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, t)]))

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(|\left(U^{2^{t - 1}}, U^{2^{t - 2}}, \ldots, U^{2^{0}}\right)|, |\left(1, 2, \ldots, t\right)|\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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