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

# build up the expression from sub-expressions
sub_expr1 = Exp(Exp(e, Neg(frac(Mult(two, pi, i, m), _two_pow_t))), k)
expr = ExprTuple(Mult(sub_expr1, Exp(e, Mult(two, pi, i, _phase, k))), Mult(sub_expr1, Exp(Exp(e, Mult(two, pi, i, _phase)), k)))

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 m}{2^{t}}})^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}, (\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot m}{2^{t}}})^{k} \cdot (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi})^{k}\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: 30 operands: 3
2	Operation	operator: 30 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 32 operands: 8
6	Operation	operator: 32 operands: 9
7	Operation	operator: 32 operands: 10
8	ExprTuple	19, 11
9	ExprTuple	12, 17
10	ExprTuple	13, 17
11	Operation	operator: 30 operands: 14
12	Operation	operator: 32 operands: 15
13	Operation	operator: 32 operands: 16
14	ExprTuple	37, 34, 35, 25, 17
15	ExprTuple	19, 18
16	ExprTuple	19, 20
17	Variable
18	Operation	operator: 21 operand: 24
19	Literal
20	Operation	operator: 30 operands: 23
21	Literal
22	ExprTuple	24
23	ExprTuple	37, 34, 35, 25
24	Operation	operator: 26 operands: 27
25	Literal
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	37, 34, 35, 36
32	Literal
33	ExprTuple	37, 38
34	Literal
35	Literal
36	Variable
37	Literal
38	Literal