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, m
from proveit.numbers import Exp, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Exp(e, Neg(frac(Mult(two, pi, i, Mod(m, _two_pow_t)), _two_pow_t))), Exp(e, Neg(frac(Mult(two, pi, i, m), _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(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}}, \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot m}{2^{t}}}\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: 28 operands: 3
2	Operation	operator: 28 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 9 operand: 11
6	Literal
7	Operation	operator: 9 operand: 12
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 27
14	Literal
15	ExprTuple	17, 27
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	30, 22, 23, 21
19	Literal
20	ExprTuple	30, 22, 23, 26
21	Operation	operator: 24 operands: 25
22	Literal
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Literal