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, t
from proveit.linear_algebra import ScalarMult
from proveit.numbers import Add, Exp, Mult, Neg, e, i, one, pi, subtract, two
from proveit.physics.quantum import ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = ExprTuple(ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1), ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, subtract(t, one)), _phase)), ket1))

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}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\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, 8
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 24 operands: 9
7	Operation	operator: 24 operands: 10
8	Operation	operator: 11 operand: 37
9	ExprTuple	13, 12
10	ExprTuple	13, 14
11	Literal
12	Operation	operator: 16 operands: 15
13	Literal
14	Operation	operator: 16 operands: 17
15	ExprTuple	27, 19, 20, 18, 22
16	Literal
17	ExprTuple	27, 19, 20, 21, 22
18	Operation	operator: 24 operands: 23
19	Literal
20	Literal
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 38 operand: 31
27	Literal
28	Operation	operator: 33 operands: 30
29	ExprTuple	31
30	ExprTuple	40, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 38 operand: 37
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	37
36	Operation	operator: 38 operand: 40
37	Literal
38	Literal
39	ExprTuple	40
40	Variable