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, l
from proveit.core_expr_types import Len
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\frac{1}{2^{t}}, \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\right)|, |\left(1, \ldots, 2\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, 7
4	Literal
5	ExprTuple	8
6	Operation	operator: 51 operands: 9
7	Operation	operator: 51 operands: 10
8	ExprRange	lambda_map: 11 start_index: 19 end_index: 58
9	ExprTuple	19, 55
10	ExprTuple	12, 13
11	Lambda	parameter: 17 body: 17
12	Operation	operator: 37 operands: 15
13	Operation	operator: 37 operands: 16
14	ExprTuple	17
15	ExprTuple	19, 18
16	ExprTuple	19, 20
17	Variable
18	Operation	operator: 45 operand: 23
19	Literal
20	Operation	operator: 45 operand: 24
21	ExprTuple	23
22	ExprTuple	24
23	Operation	operator: 56 operands: 25
24	Operation	operator: 56 operands: 26
25	ExprTuple	28, 27
26	ExprTuple	28, 29
27	Operation	operator: 42 operands: 30
28	Literal
29	Operation	operator: 42 operands: 31
30	ExprTuple	58, 33, 34, 32
31	ExprTuple	58, 33, 34, 35
32	Operation	operator: 37 operands: 36
33	Literal
34	Literal
35	Operation	operator: 37 operands: 38
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	47, 41
39	Operation	operator: 42 operands: 43
40	Operation	operator: 45 operand: 54
41	Operation	operator: 45 operand: 48
42	Literal
43	ExprTuple	55, 47
44	ExprTuple	54
45	Literal
46	ExprTuple	48
47	Operation	operator: 49 operand: 53
48	Operation	operator: 51 operands: 52
49	Literal
50	ExprTuple	53
51	Literal
52	ExprTuple	54, 55
53	Literal
54	Variable
55	Operation	operator: 56 operands: 57
56	Literal
57	ExprTuple	58, 59
58	Literal
59	Literal