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
from proveit.linear_algebra import ScalarMult, VecAdd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two, zero
from proveit.physics.quantum import Ket, ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = ExprTuple(VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k)), domain = Interval(zero, one)), 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(\sum_{k=0}^{1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle\right), \lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 44 body: 10
8	Operation	operator: 29 operand: 36
9	Operation	operator: 17 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	36
12	ExprTuple	15, 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Operation	operator: 27 operands: 21
16	Operation	operator: 29 operand: 37
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	44, 25
21	ExprTuple	34, 26
22	ExprTuple	37
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operand: 44
25	Operation	operator: 31 operands: 32
26	Operation	operator: 38 operands: 33
27	Literal
28	ExprTuple	34, 35
29	Literal
30	ExprTuple	44
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	40, 41, 42, 43
34	Literal
35	Operation	operator: 38 operands: 39
36	Literal
37	Literal
38	Literal
39	ExprTuple	40, 41, 42, 43, 44
40	Literal
41	Literal
42	Literal
43	Literal
44	Variable