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
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_round, _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, _delta_b_round, _two_pow_t))), subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round))))]), 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 \delta_{b_{\textit{r}}} \cdot 2^{t}}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}}}}\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: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprRange	lambda_map: 12 start_index: 21 end_index: 44
9	ExprTuple	21, 36
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameter: 19 body: 19
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	19
16	ExprTuple	21, 20
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Operation	operator: 24 operand: 26
21	Literal
22	Operation	operator: 24 operand: 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Operation	operator: 40 operands: 28
27	Operation	operator: 40 operands: 29
28	ExprTuple	31, 30
29	ExprTuple	31, 32
30	Operation	operator: 34 operands: 33
31	Literal
32	Operation	operator: 34 operands: 35
33	ExprTuple	44, 37, 38, 39, 36
34	Literal
35	ExprTuple	44, 37, 38, 39
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	Operation	operator: 42 operand: 46
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46
44	Literal
45	Literal
46	Literal