# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, e
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(frac(one, Exp(two, one)), _two_pow_t)

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right), -1 - e\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 9
operands: 3
2Operationoperator: 9
operands: 4
3ExprTuple5, 6
4ExprTuple7, 14
5Operationoperator: 9
operands: 8
6Operationoperator: 9
operands: 10
7Operationoperator: 17
operand: 33
8ExprTuple19, 12
9Literal
10ExprTuple13, 33, 14
11ExprTuple33
12Operationoperator: 17
operand: 32
13Operationoperator: 17
operand: 19
14Operationoperator: 17
operand: 20
15ExprTuple32
16ExprTuple19
17Literal
18ExprTuple20
19Operationoperator: 21
operands: 22
20Variable
21Literal
22ExprTuple23, 24
23Operationoperator: 25
operands: 26
24Operationoperator: 30
operands: 27
25Literal
26ExprTuple33, 28
27ExprTuple32, 29
28Operationoperator: 30
operands: 31
29Literal
30Literal
31ExprTuple32, 33
32Literal
33Literal