使用Apereo CAS的REST API来实现从一个客户端通过REST获取服务票据，并使用该票据在CAS服务器上进行身份验证和登录。

具体实现步骤如下：

1.在Apereo CAS服务器中启用REST API。可以在Apereo CAS的配置文件中添加以下配置项：

2. 在客户端中发送POST请求以获取服务票据，示例如下：

import requests

cas_api_url = "https://cas.example.com/v1/login"

# Username and password to authenticate with CAS 
username = "user"
password = "password"

# Service URL to get a ticket for
service_url = "https://myapp.example.com"

# Send a POST request to authenticate and get a service ticket
response = requests.post(cas_api_url, data={
    'username': username,
    'password': password,
    'service': service_url
})

if response.status_code == 200:
    # Extract the service ticket from the response
    service_ticket = response.content
else:
    # Handle error responses appropriately
    print("Error authenticating with CAS: {}".format(response.content))

3. 在CAS服务器上使用服务票据进行身份验证和登录，示例如下：

import requests

cas_server_url = "https://cas.example.com"
service_ticket = "ST-0123456789abcdef0123456789abcdef"

# Construct the URL to validate the service ticket
validation_url = "{}/serviceValidate?ticket={}&service={}".format(cas_server_url, service_ticket, service_url)

# Send a GET request to validate the service ticket
response = requests.get(validation_url)

if response.status_code == 200 and "" in response.content:
    # Extract the user ID from the response
    user_id = ... # extract value from XML using an appropriate library
    # Use the user ID to authenticate and/or authorize the user in the application
else:
    # Handle error responses appropriately
    print("Error validating service ticket with CAS: {}".format(response.content))

以上所示代码示例是基于Python实现的示例，其它语言的实现方式可能会有所不同。