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 Complex, 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(Mult(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))))))), Complex)

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(\frac{1}{2^{t}} \cdot \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)}}, \mathbb{C}\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: 36 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 45 operands: 6
5	Operation	operator: 45 operands: 7
6	ExprTuple	13, 49
7	ExprTuple	8, 9
8	Operation	operator: 31 operands: 10
9	Operation	operator: 31 operands: 11
10	ExprTuple	13, 12
11	ExprTuple	13, 14
12	Operation	operator: 39 operand: 17
13	Literal
14	Operation	operator: 39 operand: 18
15	ExprTuple	17
16	ExprTuple	18
17	Operation	operator: 50 operands: 19
18	Operation	operator: 50 operands: 20
19	ExprTuple	22, 21
20	ExprTuple	22, 23
21	Operation	operator: 36 operands: 24
22	Literal
23	Operation	operator: 36 operands: 25
24	ExprTuple	52, 27, 28, 26
25	ExprTuple	52, 27, 28, 29
26	Operation	operator: 31 operands: 30
27	Literal
28	Literal
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	41, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 39 operand: 48
35	Operation	operator: 39 operand: 42
36	Literal
37	ExprTuple	49, 41
38	ExprTuple	48
39	Literal
40	ExprTuple	42
41	Operation	operator: 43 operand: 47
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	47
45	Literal
46	ExprTuple	48, 49
47	Literal
48	Variable
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	Literal
53	Literal