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 ExprTuple, l
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
expr = ExprTuple(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))))))

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(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)

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: 24 operands: 3
2	Operation	operator: 24 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 32 operand: 10
6	Literal
7	Operation	operator: 32 operand: 11
8	ExprTuple	10
9	ExprTuple	11
10	Operation	operator: 43 operands: 12
11	Operation	operator: 43 operands: 13
12	ExprTuple	15, 14
13	ExprTuple	15, 16
14	Operation	operator: 29 operands: 17
15	Literal
16	Operation	operator: 29 operands: 18
17	ExprTuple	45, 20, 21, 19
18	ExprTuple	45, 20, 21, 22
19	Operation	operator: 24 operands: 23
20	Literal
21	Literal
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	34, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 32 operand: 41
28	Operation	operator: 32 operand: 35
29	Literal
30	ExprTuple	42, 34
31	ExprTuple	41
32	Literal
33	ExprTuple	35
34	Operation	operator: 36 operand: 40
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40
38	Literal
39	ExprTuple	41, 42
40	Literal
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Literal