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
from proveit.numbers import Abs, Exp, Mod, Mult, Round, four, frac, pi, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(frac(four, Exp(pi, two)), Exp(Abs(SubIndexed(_alpha, [Mod(Round(Mult(_two_pow_t, _phase)), _two_pow_t)])), 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(\frac{4}{\pi^{2}}, \left|\alpha_{round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t}}\right|^{2}\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: 3 operands: 4
2	Operation	operator: 27 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 29
6	Literal
7	Operation	operator: 27 operands: 9
8	Operation	operator: 10 operand: 13
9	ExprTuple	12, 29
10	Literal
11	ExprTuple	13
12	Literal
13	Operation	operator: 14 operand: 16
14	Literal
15	ExprTuple	16
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 25
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Literal
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Literal