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

# build up the expression from sub-expressions
expr = ExprTuple(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase)), ket1))), QubitSpace)

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{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right), \mathbb{C}^{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: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 39
6	Operation	operator: 23 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	30, 12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 37 operands: 15
13	Operation	operator: 26 operand: 20
14	Operation	operator: 17 operands: 18
15	ExprTuple	39, 19
16	ExprTuple	20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Operation	operator: 37 operands: 25
22	Operation	operator: 26 operand: 30
23	Literal
24	ExprTuple	30, 39
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Literal
29	Operation	operator: 31 operands: 32
30	Literal
31	Literal
32	ExprTuple	39, 33, 34, 35, 36
33	Literal
34	Literal
35	Operation	operator: 37 operands: 38
36	Literal
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Variable