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.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = frac(one, sqrt(two))
expr = ExprTuple(TensorProd(ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(zero)), _phase)), ket1)))), ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _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(\left[{\otimes}\right]\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\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: 3 operand: 6
2	Operation	operator: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	10, 7
6	Operation	operator: 22 operands: 8
7	Operation	operator: 14 operands: 9
8	ExprTuple	10, 11
9	ExprTuple	18, 12
10	Operation	operator: 29 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 22 operands: 16
13	ExprTuple	37, 17
14	Literal
15	ExprTuple	18, 19
16	ExprTuple	20, 27
17	Operation	operator: 44 operands: 21
18	Operation	operator: 32 operand: 50
19	Operation	operator: 22 operands: 23
20	Operation	operator: 44 operands: 24
21	ExprTuple	46, 25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	35, 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 44 operands: 31
27	Operation	operator: 32 operand: 37
28	Operation	operator: 38 operands: 34
29	Literal
30	ExprTuple	37, 46
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	37
34	ExprTuple	46, 40, 41, 43
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	46, 40, 41, 42, 43
40	Literal
41	Literal
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal