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 ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = ExprTuple(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _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(\frac{1}{\sqrt{2}}, \lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\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: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	24, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 31 operands: 9
7	Operation	operator: 20 operand: 14
8	Operation	operator: 11 operands: 12
9	ExprTuple	33, 13
10	ExprTuple	14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Operation	operator: 31 operands: 19
16	Operation	operator: 20 operand: 24
17	Literal
18	ExprTuple	24, 33
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	Literal
23	Operation	operator: 25 operands: 26
24	Literal
25	Literal
26	ExprTuple	33, 27, 28, 29, 30
27	Literal
28	Literal
29	Operation	operator: 31 operands: 32
30	Literal
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Variable